Optimal filtration for the approximation of boundary controls for the one-dimensional wave equation using a finite-difference method
Lissy, Pierre; Roventa, Ionel (2019), Optimal filtration for the approximation of boundary controls for the one-dimensional wave equation using a finite-difference method, Mathematics of Computation, 88, p. 273-291. 10.1090/mcom/3345
TypeArticle accepté pour publication ou publié
Journal nameMathematics of Computation
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Department of Mathematics [UCV]
Abstract (EN)We consider a finite-difference semi-discrete scheme for the approximation of boundary controls for the one-dimensional wave equation. The high frequency numerical spurious oscillations lead to a loss of the uniform (with respect to the mesh size) controllability property of the semi-discrete model in the natural setting. We prove that, by filtering the high frequencies of the initial data in an optimal range, we restore the uniform controllability property. Moreover, we obtain a relation between the range of filtration and the minimal time of control needed to ensure the uniform controllability. The proof is based on the moment method.
Subjects / KeywordsWave equation; control approximation; moment problem; biorthogonal families
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